First-principles investigation of the size-dependent structural stability and electronic properties of O-vacancies at the ZnO polar and non-polar surfaces
In this paper, all electron full-potential linearized augmented plane wave plus local orbitals method has been used to investigate the structural and electronic properties of polar (0001) and non-polar (10ī0) surfaces of ZnO in terms of the defect formation energy (DFE), charge density, and electronic band structure with the supercell-slab (SS) models. Our calculations support the size-dependent structural phase transformation of wurzite lattice to graphite-like structure which is a result of the termination of hexagonal ZnO at the (0001) basal plane, when the stacking of ZnO primitive cell along the hexagonal principle c-axis is less than 16 atomic layers of Zn and O atoms. This structural phase transformation has been studied in terms of Coulomb energy, nature of the bond, energy due to macroscopic electric field in the  direction, and the surface to volume ratio for the smaller SS. We show that the size-dependent phase transformation is completely absent for surfaces with a non-basal plane termination, and the resulting structure is less stable. Similarly, elimination of this size-dependent graphite-like structural phase transformation also occurs on the creation of O-vacancy which is investigated in terms of Coulomb attraction at the surface. Furthermore, the DFE at the (10ī0)/(ī010) and (0001)/(000ī) surfaces is correlated with the slab-like structures elongation in the hexagonal a- and c-axis. Electronic structure of the neutral O-vacancy at the (0001)/(000ī) surfaces has been calculated and the effect of charge transfer between the two sides of the polar surfaces (0001)/(000ī) on the mixing of conduction band through the 4s orbitals of the surface Zn atoms is elaborated. An insulating band structure profile for the non-polar (10ī0)/(ī010) surfaces and for the smaller polar (0001)/(000ī) SS without O-vacancy is also discussed. The results in this paper will be useful for the tuning of the structural and electronic properties of the (0001) and (10ī0) ZnO nanosheets by varying their size.